I know that "Would you mind… ?" (the Present Conditional) is more polite than "Do you mind…?" (the Simple Present), and also, that they have to be completed this way: "Do you mind if I do sth?/Would ...

I know that saying "I just saw her" is correct, but people also say "I've just arrived", so saying "I've just seen her" is also correct? Maybe it's a UK/US difference ?
If it's correct, then "Just" ...